Finite Group Databasebeta

#103×Dic29 #16819314

order3712
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#103×Dic29

Splittings

SylowC29 ⋊ C4×#103

Subgroups

subgroupG/H
centerC23D4×D29
commutatorC4×C29C2×C42
FrattiniC22×C4C22×D29
FittingC2×C29×#103C2
socle, prime radicalC23×C29C2×D4
cosocleC22×C4×C29C23
hypercenterC2×#103D29
hypocenterC29C4×#103
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 4332);